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Spectral gaps for light in a periodic ensemble of ultracold atoms

Mauro Antezza

Published Jan 19, 2010• 0 citations
OpenAlex

Abstract

We address the general problem of the excitation spectrum for light coupled to scatterers havingquantum fluctuating positions around the sites of a periodic lattice. In addition to providing an imaginarypart to the spectrum, we show that these quantum fluctuations affect the real part of the spectrum, in a waythat we determine analytically. Our predictions may be observed with ultracold atoms in an optical lattice,on a J 1⁄4 0 ! J0 1⁄4 1 narrow atomic transition. As a side result, we resolve a controversy for theoccurrence of a spectral gap in a fcc lattice.

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We address the general problem of the excitation spectrum for light coupled to scatterers havingquantum fluctuating positions around the sites of a periodic lattice. In addition to providing an imaginarypart to the spectrum, we show that these quantum fluctuations affect the real part of the spectrum, in a waythat we determine analytically. Our predictions may be observed with ultracold atoms in an optical lattice,on a J 1⁄4 0 ! J0 1⁄4 1 narrow atomic transition. As a side result, we resolve a controversy for theoccurrence of a spectral gap in a fcc lattice.
We address the general problem of the excitation spectrum for light coupled to scatterers havingquantum fluctuating positions around the sites of a periodic lattice. In addition to providing an imaginarypart to the spectrum, we show that these quantum fluctuations affect the real part of the spectrum, in a waythat we determine analytically. Our predictions may be observed with ultracold atoms in an optical lattice,on a J 1⁄4 0 ! J0 1⁄4 1 narrow atomic transition. As a side result, we resolve a controversy for theoccurrence of a spectral gap in a fcc lattice.
We address the general problem of the excitation spectrum for light coupled to scatterers having quantum fluctuating positions around the sites of a periodic lattice. In addition to providing an imaginary part to the spectrum, we show that these quantum fluctuations affect the real part of the spectrum, in a way that we determine analytically. Our predictions may be observed with ultracold atoms in an optical lattice, on a J = 0 --> J;{'} = 1 narrow atomic transition. As a side result, we resolve a controversy for the occurrence of a spectral gap in a fcc lattice.
We investigate theoretically light scattering of photons by ultracold atoms in an optical lattice in the linear regime. A full quantum theory for the atom-photon interactions is developed as a function of the atomic state in the lattice along the Mott-insulator--superfluid phase transition, and the photonic-scattering cross section is evaluated as a function of the energy and of the direction of emission. The predictions of this theory are compared with the theoretical results of a recent work on Bragg scattering in time-of-flight measurements [A.M. Rey et al., Phys. Rev. A 72, 023407 (2005)]. We show that, when performing Bragg spectroscopy with light scattering, the photon recoil gives rise to an additional atomic site-to-site hopping, which can interfere with ordinary tunneling of matter waves and can significantly affect the photonic-scattering cross section.
We study the light dispersion relation in a periodic ensemble of atoms at fixed positions in the Fano-Hopfield model (the atomic dipole being modeled with harmonic oscillators). Compared to earlier works, we do not restrict to cubic lattices, and we do not regularize the theory by hand but we renormalize it in a systematic way using a Gaussian cutoff in momentum space. Whereas no omnidirectional spectral gap is known for light in a Bravais atomic lattice, we find that, for a wide range of parameters, an omnidirectional gap occurs in a diamond atomic lattice, which may be realized in an experiment with ultracold atoms. The long-wavelength limit of the theory also provides a Lorentz-Lorenz (or Clausius-Mossotti) relation for an arbitrary lattice.
We study the coupling of resonant electronic excitations to vibrational center-of-mass motion of ultracold atoms in an optical lattice, when ground- and excited-state optical potentials differ. On-site excitation-vibration coupling can be approximately treated by renormalizing the effective transition energy, which appears, e.g., in lattice clock setups. In addition the dipole-dipole coupling between neighboring sites mediates emission and absorption of vibrational quanta in conjunction with optical transitions. This mechanism for excitation of vibrations can lead to significant heating of the lattice atoms motion during resonant light interaction. We calculate estimates of the corresponding parameters for a gas in the Mott-insulator state from a perturbation expansion in small atomic displacements.
We study off-resonant collective light scattering from ultracold atoms trapped in an optical lattice. Scattering from different atomic quantum states creates different quantum states of the scattered light, which can be distinguished by measurements of the spatial intensity distribution, quadrature variances, photon statistics, or spectral measurements. In particular, angle-resolved intensity measurements reflect global statistics of atoms (total number of radiating atoms) as well as local statistical quantities (single-site statistics even without optical access to a single site) and pair correlations between different sites. As a striking example we consider scattering from transversally illuminated atoms into an optical cavity mode. For the Mott-insulator state, similar to classical diffraction, the number of photons scattered into a cavity is zero due to destructive interference, while for the superfluid state it is nonzero and proportional to the number of atoms. Moreover, we demonstrate that light scattering into a standing-wave cavity has a nontrivial angle dependence, including the appearance of narrow features at angles, where classical diffraction predicts zero. The measurement procedure corresponds to the quantum nondemolition measurement of various atomic variables by observing light.